On the number of observable species, observable reactions and observable fluxes in chemometric studies and the role of multichannel integration

Garland, Marc; Visser, Erik; Terwiesch, Peter; Rippin, D.W.T.

doi:10.1016/s0003-2670(97)00213-4

Cited by 26 publications

(16 citation statements)

References 38 publications

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“…Assuming the validity of the Lambert-Beer-Bougeur-Law, A keϫv is a linear combination of a concentration matrix C keϫs (which incorporates the path length l), the pure component spectra matrix a sϫv (where s denotes number of observable species in chemical mixture), and experimental error, ⑀ keϫv [eq. (1)] 12 :…”

Section: Spectral Reconstruction Methodsmentioning

confidence: 99%

“….â s } are used, namely, angle, Euclidean inner product, determinant of covariance matrix, and condition number constraint [eqs. (11)(12)(13)(14)]. It can be noted that the latter condition number has a rather physical interpretation because the set of pure component spectral estimates corresponds to the volume of the polyhedron spanned by the L 2 normalized row vectors of â sϫv matrix.…”

Section: Dissimilarity Functionmentioning

confidence: 99%

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Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7‐species data set

Widjaja

Garland

2002

J Comput Chem

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A combination of singular value decomposition, entropy minimization, and simulated annealing was applied to a synthetic 7-species spectroscopic data set with added white noise. The pure spectra were highly overlapping. Global minima for selected objective functions were obtained for the transformation of the first seven right singular vectors. Simple Shannon type entropy functions were used in the objective functions and realistic physical constraints were imposed in the penalties. It was found that good first approximations for the pure component spectra could be obtained without the use of any a priori information. The present method out performed the two widely used routines, namely Simplisma and OPA-ALS, as well as IPCA. These results indicate that a combination of SVD, entropy minimization, and simulated annealing is a potentially powerful tool for spectral reconstructions from large real experimental systems.

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Section: Spectral Reconstruction Methodsmentioning

confidence: 99%

Section: Dissimilarity Functionmentioning

confidence: 99%

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7‐species data set

Widjaja

Garland

2002

J Comput Chem

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“…The rank of the spectral measurement matrix has been studied by Kankare [19], Cochran et al [20], Amrhein et al [21] and Garland et al [22] under batch and semi-batch conditions (strategy 3) and for the concatenation of experiments measured under different initial Chemometrics and Intelligent Laboratory Systems 95 (2009) [170][171][172][173][174][175][176][177][178][179][180][181][182][183][184][185][186][187] conditions (strategy 4). However, the effects of defining a specific absorbing species as uncoloured (strategy 1), of providing a specific component spectrum (strategy 2), of dosing a specific species (strategy 3) or of varying the initial concentrations (strategy 4) on the rank of the kinetic concentration matrix have not yet been studied in literature.…”

Section: Maeder and Zuberbühlermentioning

confidence: 99%

“…A pseudo-equivalent matrix for C under semi-batch conditions The prediction of the rank of C has been discussed in literature [15,[19][20][21][22] and requires defining the number of independent reactions [15,21]. According to Amrhein et al, the number of independent reactions, here denoted nr i , is the number of reactions that have (i) constant and linearly independent stoichiometric coefficients (rows of N), and (ii) linearly independent rate laws (columns of X).…”

Section: Rank Deficiencies In the Concentration Matrix Cmentioning

confidence: 99%

Systematic prediction of linear dependencies in the concentration profiles and implications on the kinetic hard-modelling of spectroscopic data

Billeter

Neuhold

Hungerbühler

2009

Chemometrics and Intelligent Laboratory Systems

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Hard-modelling Concentration matrix Rank deficiency and augmentation A priori information and experimental designA novel method is presented for the systematic identification of the minimum requirements regarding mathematical pre-treatment, a priori information, or experimental design, in order to allow optimising rate constants and pure component spectra associated with a kinetic model via multivariate kinetic hardmodelling of spectroscopic data. Rank deficiencies in the kinetic concentration matrix represent a major problem for the calibration free method developed by Maeder and Zuberbühler, as its pseudo-inverse, required for the optimisation process, is not defined. In this contribution, the underlying linear dependencies in the concentration profiles are systematically elucidated and appropriate strategies are discussed in order to break them. Also, conditions are predicted for which full spectral resolution can be expected. The method is based on the kernel of a time invariant augmented matrix covering potential rank deficiency due to stoichiometry and rate laws, also relevant for the concentration matrix. Compared to employing the full concentration matrix, this augmented matrix does not require a numerical integration of the differential equations describing the kinetic model and thus can easily be set up. The kernel can be calculated numerically by Singular Value Decomposition (SVD) or determined in a symbolical way, the latter allowing the detection of particular stoichiometric conditions leading to spectral resolution of species. The capabilities of the method are demonstrated analysing three kinetic mechanisms of increasing complexity covering consecutive and parallel reactions.

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“…Perform singular value decomposition (SVD) of spectroscopic data array A k؋ where k is the number of experiments taken, is the number of spectroscopic data channels (k Ͻ ). After truncating the physical meaningless parts of right singular matrix V T ϫ and zero part of diagonal matrix ⌺ k؋ , they reduced to V T kϫ and ⌺ k؋k [22][23][24].…”

Section: Overall Tbtem Algorithmmentioning

confidence: 99%

Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: Simulation studies and the application to real systems

Zhang

Garland

Zeng

et al. 2003

J. Am. Soc. Mass Spectrom.

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A method is proposed, on the basis of a recently developed algorithm-Band Target Entropy Minimization (BTEM)-to reconstruct mass spectra of pure components from mixture spectra. This method is particular useful in dealing with spectral data with discrete features (like mass spectra). Compared to the original BTEM, which has been applied to differentiable spectroscopies such as Fourier-transfer infrared spectroscopy (FTIR), ultraviolet (UV), Raman, and nuclear magnetic resonance (NMR), the latest modifications were obtained through: (1) Reformulating the objective function using the peak heights instead of their derivatives; (2) weighting the abstract vector V T to reduce the effect of noise; (3) using a two-peak targeting strategy (tBTEM) to deal with strongly overlapping peaks; and (4) using exhaustive search to locate all the component spectra. A set of 50 multi-component mass spectra was generated from ten reference experimental pure component spectra. Many of the compounds chosen have common MS fragments and therefore, many of the pure component spectra have considerable intensity in same data channels. In addition, a set of MS spectra from a real system with four components was used to examine the newly developed algorithm. Successful reconstruction of the ten component spectra of the simulated system and the four component spectra of the real system was rapidly achieved using the new tBTEM algorithm. The advantages of the new algorithm and its implication for rapid system identification of unknown mixtures are readily apparent. (J

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On the number of observable species, observable reactions and observable fluxes in chemometric studies and the role of multichannel integration

Cited by 26 publications

References 38 publications

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7‐species data set

Pure component spectral reconstruction from mixture data using SVD, global entropy minimization, and simulated annealing. Numerical investigations of admissible objective functions using a synthetic 7‐species data set

Systematic prediction of linear dependencies in the concentration profiles and implications on the kinetic hard-modelling of spectroscopic data

Weighted two-band target entropy minimization for the reconstruction of pure component mass spectra: Simulation studies and the application to real systems

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